Population Prediction and Exponential Functions

The video tutorial explains how to model the population growth of a small town using an exponential function. Starting with a population of 32,000 in 2012, the town's population grows at an annual rate of 2.8%. The function P(t) = 32 * 1.28^t is used, where P(t) is the population in thousands and t is the number of years since 2012. The tutorial demonstrates how to calculate the population in 2030 by determining the value of t as 18, using a calculator to compute P(18), and interpreting the result as approximately 52,600 people, rounded to the nearest 100.

What was the initial population of the town in 2012?

• 36,000

• 30,000

• 32,000

• 34,000

At what annual rate is the town's population growing?

• 2.8%

• 2.5%

• 3.0%

• 3.2%

What is the base year used in the exponential function for population prediction?

• 2012

• 2011

• 2013

• 2010

How do you calculate the value of T for the year 2030?

• Divide 2030 by 2012

• Add 18 to 2012

• Subtract 2012 from 2030

• Multiply 18 by 2030

What is the value of T for the year 2030?

• 17

• 18

• 19

• 16

Which key is used on the calculator to raise a number to a power?

• Subtraction key

• Exponent key

• Division key

• Addition key

What is the approximate population in thousands for the year 2030 before rounding?

• 50.6

• 51.6

• 52.6

• 53.6

What is the population prediction for 2030 rounded to the nearest hundred?

• 52,700

• 52,500

• 52,600

• 52,800

In what unit is the population expressed in the exponential function?

• Hundreds

• Thousands

• Millions

• Billions

What is the final prediction for the population in 2030 expressed in a complete sentence?

• The population in 2030 is approximately 52,500.

• The population in 2030 is approximately 52,600.

• The population in 2030 is approximately 52,700.

• The population in 2030 is approximately 52,800.